basic reproduction number


Summary: The expected number of new cases of an infection caused by an infected individual, in a population consisting of susceptible contacts only.

Top Publications

  1. Zhang J, Jin Z, Sun G, Sun X, Ruan S. Modeling seasonal rabies epidemics in China. Bull Math Biol. 2012;74:1226-51 pubmed publisher
    ..We evaluate the basic reproduction number R (0), analyze the dynamical behavior of the model, and use the model to ..
  2. Arino J, Brauer F, van den Driessche P, Watmough J, Wu J. A model for influenza with vaccination and antiviral treatment. J Theor Biol. 2008;253:118-30 pubmed publisher
    ..Analytic expressions for the basic reproduction number, control reproduction number and the final size of the epidemic are derived for this general class of ..
  3. Bacaer N, Ait Dads E. On the biological interpretation of a definition for the parameter R? in periodic population models. J Math Biol. 2012;65:601-21 pubmed publisher
    An adaptation of the definition of the basic reproduction number R (0) to time-periodic seasonal models was suggested a few years ago. However, its biological interpretation remained unclear...
  4. Klinkenberg D, Nishiura H. The correlation between infectivity and incubation period of measles, estimated from households with two cases. J Theor Biol. 2011;284:52-60 pubmed publisher
    ..g. in estimating the basic reproduction number. Moreover, the generation time and incubation period distributions together characterize the ..
  5. Bacaer N. Approximation of the basic reproduction number R0 for vector-borne diseases with a periodic vector population. Bull Math Biol. 2007;69:1067-91 pubmed
    The main purpose of this paper is to give an approximate formula involving two terms for the basic reproduction number R(0) of a vector-borne disease when the vector population has small seasonal fluctuations of the form p(t) = p(0) (1+..
  6. Ball F, Sirl D, Trapman P. Analysis of a stochastic SIR epidemic on a random network incorporating household structure. Math Biosci. 2010;224:53-73 pubmed publisher
    ..The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored. ..
  7. Vargas de León C. Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes. Math Biosci Eng. 2012;9:165-74 pubmed publisher
    ..If R?(?) > 1 a unique endemic equilibrium exists and is globally asymptotically stable. We apply our results to Ross-MacDonald malaria models with an incubation period (extrinsic or intrinsic)...
  8. Griffin J, Garske T, Ghani A, Clarke P. Joint estimation of the basic reproduction number and generation time parameters for infectious disease outbreaks. Biostatistics. 2011;12:303-12 pubmed publisher
    The basic reproduction number is a key parameter determining whether an infectious disease will persist...
  9. Gubbins S, Hartemink N, Wilson A, Moulin V, Vonk Noordegraaf C, van der Sluijs M, et al. Scaling from challenge experiments to the field: Quantifying the impact of vaccination on the transmission of bluetongue virus serotype 8. Prev Vet Med. 2012;105:297-308 pubmed publisher
    ..The results of the challenge studies for calves indicated that vaccination is likely to reduce the basic reproduction number (R(0)) for BTV in cattle to below one (i.e...

More Information


  1. Tanner M, Sattenspiel L, Ntaimo L. Finding optimal vaccination strategies under parameter uncertainty using stochastic programming. Math Biosci. 2008;215:144-51 pubmed publisher
    ..Results derived from a stochastic programming analysis can also help to guide decisions about how much effort and resources to focus on collecting data needed to provide better estimates of key parameters. ..
  2. Bacaer N, Ait Dads E. Genealogy with seasonality, the basic reproduction number, and the influenza pandemic. J Math Biol. 2011;62:741-62 pubmed publisher
    The basic reproduction number R (0) has been used in population biology, especially in epidemiology, for several decades. But a suitable definition in the case of models with periodic coefficients was given only in recent years...
  3. Rubel F, Brugger K, Hantel M, Chvala Mannsberger S, Bakonyi T, Weissenbock H, et al. Explaining Usutu virus dynamics in Austria: model development and calibration. Prev Vet Med. 2008;85:166-86 pubmed publisher
    ..Vet. Microbiol. 122, 237-245]. These results suggest that the model presented is able to quantitatively describe the process of USUV dynamics. ..
  4. Bacaer N, Ouifki R. Growth rate and basic reproduction number for population models with a simple periodic factor. Math Biosci. 2007;210:647-58 pubmed
    ..population models with a periodic factor which is sinusoidal, both the growth rate and the basic reproduction number are shown to be the largest roots of simple equations involving continued fractions...
  5. Sun H, Lu X, Ruan S. Qualitative analysis of models with different treatment protocols to prevent antibiotic resistance. Math Biosci. 2010;227:56-67 pubmed publisher
    ..about the local or global stability of the equilibria of both models is carried out in term of the basic reproduction number R(0)...
  6. Hens N, Van Ranst M, Aerts M, Robesyn E, Van Damme P, Beutels P. Estimating the effective reproduction number for pandemic influenza from notification data made publicly available in real time: a multi-country analysis for influenza A/H1N1v 2009. Vaccine. 2011;29:896-904 pubmed publisher
    ..In this paper, we show how and in which situations the recorded history of cumulated case counts provides valuable information to estimate the effective reproductive number in an early phase and for a large number of countries. ..
  7. de Camino Beck T, Lewis M, van den Driessche P. A graph-theoretic method for the basic reproduction number in continuous time epidemiological models. J Math Biol. 2009;59:503-16 pubmed publisher
    In epidemiological models of infectious diseases the basic reproduction number 'R(0) is used as a threshold parameter to determine the threshold between disease extinction and outbreak...
  8. Nishiura H. Time variations in the generation time of an infectious disease: implications for sampling to appropriately quantify transmission potential. Math Biosci Eng. 2010;7:851-69 pubmed publisher epidemic of Asian influenza A (H2N2) in the Netherlands in 1957 was reanalyzed, and estimates of the basic reproduction number, , from the Lotka-Euler equation were examined...
  9. Diekmann O, Heesterbeek J, Roberts M. The construction of next-generation matrices for compartmental epidemic models. J R Soc Interface. 2010;7:873-85 pubmed publisher
    The basic reproduction number (0) is arguably the most important quantity in infectious disease epidemiology...
  10. White L, Wallinga J, Finelli L, Reed C, Riley S, Lipsitch M, et al. Estimation of the reproductive number and the serial interval in early phase of the 2009 influenza A/H1N1 pandemic in the USA. Influenza Other Respir Viruses. 2009;3:267-76 pubmed publisher
  11. Safi M, Imran M, Gumel A. Threshold dynamics of a non-autonomous SEIRS model with quarantine and isolation. Theory Biosci. 2012;131:19-30 pubmed publisher
  12. Balcan D, Hu H, Goncalves B, Bajardi P, Poletto C, Ramasco J, et al. Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility. BMC Med. 2009;7:45 pubmed publisher
    ..We suggest that the planning of additional mitigation policies such as systematic antiviral treatments might be the key to delay the activity peak in order to restore the effectiveness of the vaccination programs. ..
  13. Coburn B, Wagner B, Blower S. Modeling influenza epidemics and pandemics: insights into the future of swine flu (H1N1). BMC Med. 2009;7:30 pubmed publisher
    ..We discuss how the feasibility of controlling an epidemic critically depends on the value of the Basic Reproduction Number (R0). The R0 for novel influenza A (H1N1) has recently been estimated to be between 1.4 and 1.6...
  14. Korobeinikov A. Global properties of SIR and SEIR epidemic models with multiple parallel infectious stages. Bull Math Biol. 2009;71:75-83 pubmed publisher
    ..Depending on the value of the basic reproduction number R0, this state can be either endemic (R0>1), or infection-free (R0< or =1).
  15. Hartemink N, Randolph S, Davis S, Heesterbeek J. The basic reproduction number for complex disease systems: defining R(0) for tick-borne infections. Am Nat. 2008;171:743-54 pubmed publisher
    Characterizing the basic reproduction number, R(0), for many wildlife disease systems can seem a complex problem because several species are involved, because there are different epidemiological reactions to the infectious agent at ..
  16. Trapman P. Reproduction numbers for epidemics on networks using pair approximation. Math Biosci. 2007;210:464-89 pubmed
    ..Furthermore, in literature problems arise in defining basic quantities like the basic reproduction number R(0) and the real-time epidemic growth rate parameter r...
  17. Nishiura H, Yan P, Sleeman C, Mode C. Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks. J Theor Biol. 2012;294:48-55 pubmed publisher
  18. Rebelo C, Margheri A, Bacaer N. Persistence in seasonally forced epidemiological models. J Math Biol. 2012;64:933-49 pubmed publisher
    ..In this paper we address the persistence of a class of seasonally forced epidemiological models. We use an abstract theorem about persistence by Fonda. Five different examples of application are given. ..
  19. Wesley C, Allen L. The basic reproduction number in epidemic models with periodic demographics. J Biol Dyn. 2009;3:116-29 pubmed publisher
    ..No general method exists for calculating the basic reproduction number, the threshold for disease extinction, in nonautonomous epidemic models...
  20. Vynnycky E, Edmunds W. Analyses of the 1957 (Asian) influenza pandemic in the United Kingdom and the impact of school closures. Epidemiol Infect. 2008;136:166-79 pubmed
    ..and clinical data from the United Kingdom from the 1957 (Asian) influenza pandemic, to estimate the basic reproduction number (R0), the proportion of infected individuals who experience clinical symptoms and the impact of school/..
  21. House T, Keeling M. Household structure and infectious disease transmission. Epidemiol Infect. 2009;137:654-61 pubmed publisher
    ..Since these benefits of childhood vaccination are a product of correlations between household size and number of dependent children in the household, our results are qualitatively robust for a variety of disease scenarios. ..
  22. Hosack G, Rossignol P, van den Driessche P. The control of vector-borne disease epidemics. J Theor Biol. 2008;255:16-25 pubmed publisher
    ..underpinning of our struggle with vector-borne disease, and still our strongest tool, remains the basic reproduction number, R(0), the measure of long term endemicity...
  23. House T, Keeling M. Epidemic prediction and control in clustered populations. J Theor Biol. 2011;272:1-7 pubmed publisher
  24. Gran J, Wasmuth L, Amundsen E, Lindqvist B, Aalen O. Growth rates in epidemic models: application to a model for HIV/AIDS progression. Stat Med. 2008;27:4817-34 pubmed publisher
    ..common quantity used to describe the growth of an epidemic when modelling infectious diseases is the basic reproduction number R0...
  25. Kamgang J, Sallet G. Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE). Math Biosci. 2008;213:1-12 pubmed publisher
    ..sufficient condition for the global asymptotic stability of the DFE is R(0)< or =1, where R(0) is the basic reproduction number [O. Diekmann, J.A...
  26. Chowell G, Fuentes R, Olea A, Aguilera X, Nesse H, Hyman J. The basic reproduction number R0 and effectiveness of reactive interventions during dengue epidemics: the 2002 dengue outbreak in Easter Island, Chile. Math Biosci Eng. 2013;10:1455-74 pubmed publisher
    ..reported prior to 2002 in Easter Island, the 2002 epidemic provided a unique opportunity to estimate the basic reproduction number R0 during the initial epidemic phase, prior to the start of control interventions. We estimated R0 at 27...
  27. Beretta E, Breda D. An SEIR epidemic model with constant latency time and infectious period. Math Biosci Eng. 2011;8:931-52 pubmed publisher
    ..e. the disease-free equilibrium E0 and the positive equilibrium E+, which exists iff the basic reproduction number R0 is larger than one. If R0 > 1 we also provide a permanence result for the model solutions...
  28. Mwasa A, Tchuenche J. Mathematical analysis of a cholera model with public health interventions. Biosystems. 2011;105:190-200 pubmed publisher
    ..numbers R(E), R(V), R(T) respectively and the combined reproductive number R(C) are compared with the basic reproduction number R(0) to assess the possible community benefits of these control measures...
  29. Pellis L, Ferguson N, Fraser C. Epidemic growth rate and household reproduction number in communities of households, schools and workplaces. J Math Biol. 2011;63:691-734 pubmed publisher
    ..g. reproduction numbers, critical vaccination coverage, epidemic final size) to new results on the epidemic dynamics. ..
  30. Dumont Y, Chiroleu F. Vector control for the Chikungunya disease. Math Biosci Eng. 2010;7:313-45 pubmed publisher
  31. Liu L, Zhao X, Zhou Y. A tuberculosis model with seasonality. Bull Math Biol. 2010;72:931-52 pubmed publisher
    ..Parameter values of the model are estimated according to demographic and epidemiological data in China. The simulation results are in good accordance with the seasonal variation of the reported cases of active TB in China. ..
  32. Bacaer N. Periodic matrix population models: growth rate, basic reproduction number, and entropy. Bull Math Biol. 2009;71:1781-92 pubmed publisher
    ..Secondly, the formula for the basic reproduction number R0 in a constant environment is generalized to the case of a periodic environment...
  33. Stoddard S, Morrison A, Vazquez Prokopec G, Paz Soldan V, Kochel T, Kitron U, et al. The role of human movement in the transmission of vector-borne pathogens. PLoS Negl Trop Dis. 2009;3:e481 pubmed publisher
    ..Understanding movement will facilitate identification of key individuals and sites in the transmission of pathogens such as dengue, which then may provide targets for surveillance, intervention, and improved disease prevention. ..
  34. Ma E, Fung C, Yip S, Wong C, Chuang S, Tsang T. Estimation of the basic reproduction number of enterovirus 71 and coxsackievirus A16 in hand, foot, and mouth disease outbreaks. Pediatr Infect Dis J. 2011;30:675-9 pubmed publisher
    ..This finding helps better understand the transmission dynamics of HFMD outbreaks and formulate public health measures for controlling the disease. ..
  35. Massad E, Coutinho F. Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations. Mem Inst Oswaldo Cruz. 2012;107:564-7 pubmed
    ..The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors. ..
  36. Cross P, Johnson P, Lloyd Smith J, Getz W. Utility of R0 as a predictor of disease invasion in structured populations. J R Soc Interface. 2007;4:315-24 pubmed
  37. Inaba H. On a new perspective of the basic reproduction number in heterogeneous environments. J Math Biol. 2012;65:309-48 pubmed publisher
    Although its usefulness and possibility of the well-known definition of the basic reproduction number R0 for structured populations by Diekmann, Heesterbeek and Metz (J Math Biol 28:365-382, 1990) (the DHM definition) have been widely ..
  38. Goldstein E, Paur K, Fraser C, Kenah E, Wallinga J, Lipsitch M. Reproductive numbers, epidemic spread and control in a community of households. Math Biosci. 2009;221:11-25 pubmed publisher
    ..Along the way, we have also shown that in choosing between increasing vaccine efficacy and increasing coverage levels by the same factor, preference should go to efficacy. ..
  39. Greenhalgh S, Galvani A, Medlock J. Disease elimination and re-emergence in differential-equation models. J Theor Biol. 2015;387:174-80 pubmed publisher
  40. Glass K, Mercer G, Nishiura H, McBryde E, Becker N. Estimating reproduction numbers for adults and children from case data. J R Soc Interface. 2011;8:1248-59 pubmed publisher
  41. Ogbunugafor C, Basu S, Morales N, Turner P. Combining mathematics and empirical data to predict emergence of RNA viruses that differ in reservoir use. Philos Trans R Soc Lond B Biol Sci. 2010;365:1919-30 pubmed publisher
  42. Zhang J, Jin Z, Sun G, Zhou T, Ruan S. Analysis of rabies in China: transmission dynamics and control. PLoS ONE. 2011;6:e20891 pubmed publisher
    ..We estimate that the basic reproduction number R? = 2 for the rabies transmission in China and predict that the number of the human rabies is ..
  43. Chua T. Modelling the effect of temperature change on the extrinsic incubation period and reproductive number of Plasmodium falciparum in Malaysia. Trop Biomed. 2012;29:121-8 pubmed
    ..A temperature increase arising from the global climate change will likely affect the epidemiology of malaria in Malaysia, especially in the cooler areas. ..
  44. Spicknall I, Foxman B, Marrs C, Eisenberg J. A modeling framework for the evolution and spread of antibiotic resistance: literature review and model categorization. Am J Epidemiol. 2013;178:508-20 pubmed publisher
    ..Thus, even if all parameter values are correctly estimated, inferences may be incorrect because of the incorrect selection of model structure. Our framework provides insight into model selection. ..
  45. Hashmi S. La Gloria, Mexico: the possible origins and response of a worldwide H1N1 flu pandemic in 2009. Am J Disaster Med. 2013;8:57-64 pubmed publisher
    ..As a result of this study, we conclude that, with strict government measures to control the disease over an extended period of time, it is possible that many hundreds or even thousands of lives might be saved in the future. ..
  46. Chen Z, Zou L, Shen D, Zhang W, Ruan S. Mathematical modelling and control of schistosomiasis in Hubei Province, China. Acta Trop. 2010;115:119-25 pubmed publisher
    ..After analyzing the existence of the disease-free equilibrium of the model, we determine the basic reproduction number and use the model to simulate the schistosomiasis infection data from Hubei Province...
  47. Edwards R, Kim S, van den Driessche P. A multigroup model for a heterosexually transmitted disease. Math Biosci. 2010;224:87-94 pubmed publisher
    ..These two cases are illustrated with parameters applicable to gonorrhea in the US. ..
  48. Ogunjimi B, Hens N, Goeyvaerts N, Aerts M, Van Damme P, Beutels P. Using empirical social contact data to model person to person infectious disease transmission: an illustration for varicella. Math Biosci. 2009;218:80-7 pubmed publisher
    ..model estimation methods in how well they fitted seroprevalence data and produced estimates for the basic reproduction number R(0) and the effective vaccination level required for elimination of varicella...
  49. Bate A, Hilker F. Predator-prey oscillations can shift when diseases become endemic. J Theor Biol. 2013;316:1-8 pubmed publisher
    ..These findings undermine any R(0) analysis based solely on steady states when predator-prey oscillations exist for density dependent diseases. ..
  50. Beggs C, Noakes C, Shepherd S, Kerr K, Sleigh P, Banfield K. The influence of nurse cohorting on hand hygiene effectiveness. Am J Infect Control. 2006;34:621-6 pubmed
    ..The study demonstrates that applying strict nurse cohorting in combination with good hygiene practice is likely to be a more effective method of reducing transmission of infection in hospitals. ..
  51. Inaba H. Endemic threshold results in an age-duration-structured population model for HIV infection. Math Biosci. 2006;201:15-47 pubmed
    ..Finally, we show sufficient conditions for the local stability of the endemic steady states. ..
  52. Lee J, Choi D, Cho G, Kim Y. The effect of public health interventions on the spread of influenza among cities. J Theor Biol. 2012;293:131-42 pubmed publisher
    ..First we obtain the basic reproduction number for the single city case, and observe two other control strategies suggested by this case: increasing ..
  53. Kenah E. Contact intervals, survival analysis of epidemic data, and estimation of R(0). Biostatistics. 2011;12:548-66 pubmed publisher
    ..Estimates of the contact interval distribution can be used to estimate R(0) in both mass-action and network-based models. We apply these methods to 2 data sets from the 2009 influenza A(H1N1) pandemic. ..